HI guys: I am trying to put the permutation and combination in my head but still have problem to figure it out if the problem is about P or C. I have a question and the answer of that question is P(9,5). I just want to know how i know its a permutation or combination by just looking at the problem. I understand that permutation means order matters and combination means order doesnt.
There are nine empty seats in a theater, and five customers need to find places to sit. How many different ways can these five seat themselves ?
There are nine empty seats in a theater, and five basketballs you need to store in them.
How many different ways can you arrange the basketballs ?
This is slightly tricky. People are different, so order matters. Basketballs are the same so it doesn't.
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Thibault St john Cholmondeley-ffeatherstonehaugh the 2ndCommented:
>understand the difference between them
Try with small numbers, higher than 6 items and the numbers get so large you get lost in the fog.
Take three items, a, b and c.
I can make three pairs from these items, ab, ac and bc <- those are three combinations.
If the order matters, such as how this pair sit in a theatre then I have six different arrangements because I can reverse the pairs:ab, ba, ac, ca, bc and cb <-these are permutations and there are more of them because I don't only find the number of groups, but I find how many ways these groups can be arranged within themselves.
Just as a start at taking three from four items, there are four groups (abc, abd, acd, bcd) <- combinations.
To find number of permutations I also need to multiply by the number of arrangements of each of the three unique groups. for each group there are 6 perms (abc, acb, bac, bca, cab, cba) etc.
So picking three from four gives four combinations, but 6x4 permutations.
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mustish1Author Commented:
Thanks RobinD
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so permutation (9,5) is 9x8x7x6x5.
Combination would be like asking how many pairs of people can you make from those 5. which would be (5x4)/(2x1)